WiFi is free, on free WiFi networks such as your home or free hotspots. On the iPhone, when the band signal (same as on a computer) is illuminated, it is connected to a WiFi network. My understanding is that when connected to WiFi, it takes precedence over the Verizon 3G data, so you shouldn't have any worries at home.

Downside is leaving the WiFi on all the time looking for a network appears to be a drain on the battery for an iPhone, would guess Android is similar but obviously I'm not certain._________________2.3 GHz i7 Mini (stock)
2.6 GHz i7 Mini, Samsung 830 & Hitachi
15" 2.3 GHz i7 MBP, Samsung 840 & WD Black
3.5GHz 6C MP, D700s

You're correct that Verizon's data plans are expensive for what you get. But I think, the purpose of using data on a mobile device for most people is to have it available on the go, away from home. Besides, without data from your carrier, it will limit the usability of many apps that use data and even gps. Without having data on a smart phone, it really limits its capability and reduces it down to a dumb phone. I haven't checked into what Verizon is offering lately, but some carriers require data plans with some smart phones. If you're looking to save money, you may want to take a look at your plan(s) and see if you're actually using all that you're paying for. If not, you may be able to save some $$$ by switching to a less expensive plan. Also, Verizon does offer employee discounts if you work for specific employers and for certain affiliations like credit unions.

Similar to an iPad or iPhone it should (read your manual) automatically indicate when a Wi-Fi network is present and then give you the choice to connect to that Wi-Fi network (generally a password will be required to join the Wi-Fi network). Once you have connected to the Wi-Fi network the phone will remember that Wi-Fi network an automatically connect you to that network when ever you are within range of that network.
Once you leave a known Wi-Fi network you are then automatically on the 3G network. There is no need to be constantly turning Wi-Fi and 3G on/off. It's an automatic process.
Learn the symbols on your phone. It will indicate through a symbol what it is connecting to.